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<span class="kw">let </span><font color="Maroon" title="c2">X0</font> be    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X0</font> is  <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a>  &amp; <font color="Maroon" title="c2">X0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  implies  not <font color="Maroon" title="c2">X0</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>  )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="tsp_2.html#E19"><span class="lab"><font color="Green" title="E15">Lm1</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:21_6_1"/>
<font color="Maroon" title="c2">X0</font> is  <a href="borsuk_1.html#V1" title="BORSUK_1:attr.1">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">X0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>  or  not <font color="Maroon" title="c2">X0</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>  )</span><br/>

<a NAME="E3:21_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<font color="Maroon" title="c3">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T11" title="TSEP_1:th.11">TSEP_1:11</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:21_6_1"/>
<font color="Maroon" title="c2">X0</font> is  <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c2">X0</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> </span><br/>

<a NAME="E5:21_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">A</font> is  <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_2.html#T11" target="_self" title="TSP_2:th.11">Th11</a></span>;<br/>
<a NAME="E6:21_6_1"/><span class="kw">then </span>
not <font color="Maroon" title="c3">A</font> is  <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21_6_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="tsp_2.html#T3" target="_self" title="TSP_2:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:21_6_1"/>
not <font color="Maroon" title="c2">X0</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tex_2.html#T13" title="TEX_2:th.13">TEX_2:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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